Buckling-constrained structural design problems have conventionally prioritized optimizing the buckling load factor with less consideration given to the buckling mode shape. In this work, mode shape constraints are imposed within a topology optimization problem using an eigenvector aggregate constraint that is a weighted sum of homogeneous quadratic functions of the linearized buckling eigenvectors. A generalized formulation of the eigenvector aggregate is introduced, extending previous work. A new adjoint-based derivative evaluation technique is derived that is valid even in the presence of repeated eigenvalues. Numerical examples, including a clamped beam, a compressed column, and a square plate, demonstrate the effectiveness of the proposed approach. The results show the ability of the eigenvector aggregate to handle repeated eigenvalues, enable design space exploration, and capture mode shape switching.

中文翻译：

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使用特征向量聚合进行拓扑优化的屈曲模式约束


屈曲约束结构设计问题通常优先考虑优化屈曲载荷系数，而很少考虑屈曲模态形状。在这项工作中，使用特征向量聚合约束在拓扑优化问题中施加振型约束，该特征向量聚合约束是线性化屈曲特征向量的齐次二次函数的加权和。引入了特征向量聚合的广义公式，扩展了之前的工作。推导了一种新的基于伴随的导数评估技术，即使存在重复特征值，该技术也是有效的。数值例子，包括夹紧梁、压缩柱和方形板，证明了所提出方法的有效性。结果显示了特征向量聚合处理重复特征值、实现设计空间探索和捕获模式形状切换的能力。